Class FloatComplexCholeskyLeastSq solves least square problems by using
the Cholesky factorization to solve the normal equations.
Namespace:
CenterSpace.NMath.MatrixAssembly: NMath (in NMath.dll) Version: 5.1.0.0
Syntax
| C# |
|---|
[SerializableAttribute] public class FloatComplexCholeskyLeastSq : ICloneable |
| Visual Basic (Declaration) |
|---|
<SerializableAttribute> _ Public Class FloatComplexCholeskyLeastSq _ Implements ICloneable |
| Visual C++ |
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[SerializableAttribute] public ref class FloatComplexCholeskyLeastSq : ICloneable |
Remarks
The normal equations for the least squares problem
Ax = b are:
CopyC#
where A' denotes the transpose of the matrix A.
If A has full rank, then A'A is symmetric
positive definite (and, in fact, the converse is true). Thus, the
Cholesky factorization may be used to solve the normal equations.
Note this implies that this method will fail if A is
rank deficiennt.
A'Ax = A'b